The best way to see what's available for hurricane haulout or for slips is to contact the marinas I suggested directly. I can't keep track of their policies, another subject all together!
If you are in the marina I think the odds of theft are very small. Most people know who belongs and who doesn't. There are very good yacht management services that could check your bilges, batteries, lines, etc. on a schedule for a fee. If you wanted to have your boat hauled for a named storm, I'm sure that could be arranged too from the states before you head down. The vast majority of people with boats in the slips do not haul their boats for storms. Being away from your boat for 45 days at a time shouldn't be an issue except when a storm is coming.
There is a hospital on Island that can handle most things. Major spinal injuries, major burns etc. get jetted off to Miami for treatment. You can Google Schneider Hospital and see what is written. There are numerous drugstores, a Walgreens just opened a week ago, so getting prescriptions filled isn't a big deal. There is a VA Hospital on Puerto Rico. I don't know much about the VA stuff.
I also just checked flights. It looks like Tallahassee is the nearest airport to you. Looking out just 2 weeks I'm seeing round trip prices on Kayak for around $700 round trip. Are you flying first class or taking a limo service to Miami?